In compilers, there's been a recent uptick in industry research and adoption into using equivalency classes and graphs (egraphs) for doing optimization passes in a way that preserves information and solves the phase ordering problem. Egg[0] was one of the big libraries that came out of it, but can only handle term rewriting without guards, and so can't express y/x*x -> y because it's unsound when x=0, or optimization passes that are across control flow points and thus some of the eclasses are only valid in some locations. The Cranelift developers adapted it into a construction they call aegraphs[1] that handles this, and are migrating Cranelift to use these passes for all optimizations, which is (hopefully) faster and achieves more optimization opportunitie; Chris Fallin is presenting about their aegraph work at PLDI this year.
0: https://egraphs-good.github.io/
1: https://github.com/cfallin/rfcs/blob/main/accepted/cranelift...